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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Let's try together: Solve x − 4 = 9. Is x being added or subtracted? It is subtracted, so the inverse is adding 4 to both sides. x = 9 + 4 = 13. Check together: 13 − 4 = 9. True?

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartWhich equation represents: 'Three times a number equals 21'?

   1. An + 3 = 21
   2. Bn − 3 = 21
   3. C3n = 21
   4. Dn / 3 = 21
3. 3

   Warm restartWhich equation represents: 'Seven less than a number is 18'?

   1. A7 − n = 18
   2. Bn − 7 = 18
   3. Cn + 7 = 18
   4. Dn / 7 = 18
4. 4

   Warm restartWhich equation represents: 'A number plus 12 equals 30'?

   1. An − 12 = 30
   2. B12n = 30
   3. Cn + 12 = 30
   4. Dn / 12 = 30

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughSolve d + 4.5 = 12.

   1. Ad = 7.5
   2. Bd = 16.5
   3. Cd = 8.5
   4. Dd = 4.5

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughWhich operation undoes addition?

   1. ASubtraction
   2. BMultiplication
   3. CDivision
   4. DSquaring

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughCheck: does 7.5 work?

   1. AYes — 7.5 + 4.5 = 12
   2. BNo — 7.5 + 4.5 = 11
   3. CNo — 7.5 − 4.5 = 3
   4. DOnly if the trail is 11 miles

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelWhy do you have to subtract 19 from BOTH sides, not just one?

   I subtract from both sides because an equation is like a ___ — to keep it balanced, any operation on one side must ___.

Use the words

Fill each blank with a word from the bank.

• Undo an addition by ___ the same amount from both sides.
• A math sentence with an equal sign showing two equal amounts is an ___.
• An operation that undoes another, like subtraction undoing addition, is an ___.
• To get the variable alone on one side of the equation is to ___ it.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake is applying the same operation instead of the inverse — for example, solving x − 7 = 15 by subtracting 7 from both sides (getting the wrong x = 8) instead of adding 7 to both sides (the correct x = 22).
2. 10

   Say moreWhat inverse operation did you use to solve n + 23 = 58, and why must you do it to BOTH sides of the balance?

   I used ___ to undo ___, so the variable equals ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   Show your work

Last check

These two come from Lesson 8.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Solve: p + 2.8 = 9.1

   1. Ap = 6.3
   2. Bp = 11.9
   3. Cp = 7.7
   4. Dp = 3.25

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 8.1Quick check — you've got this: Which value is the solution of n + 5 = 9, and how do you know?

   1. An = 4, because 4 + 5 = 9 is true
   2. Bn = 14, because 9 + 5 = 14
   3. Cn = 3, because 3 is close to 4
   4. Dn = 5, because 5 appears in the equation
3. 14

   From Lesson 8.1Check your answer: does 23 work?

   1. AYes — 23 + 14 = 37
   2. BNo — 23 + 14 = 47
   3. CNo — 23 − 14 = 9
   4. DYou cannot check an equation

Be honest — this tells your teacher what to do next